A comparative study of dynamical simulation methods for the dissociation of molecular Bose-Einstein condensates

TL;DR

This paper compares three different simulation methods for modeling the dissociation of molecular Bose-Einstein condensates, highlighting their accuracy, limitations, and the effects of atom-atom interactions.

Contribution

It introduces a pairing mean-field theory and evaluates its performance against stochastic phase-space techniques in simulating molecular BEC dissociation.

Findings

Truncated Wigner method agrees with positive-P for longer times

Pairing mean-field theory diverges quickly from quantum methods

Atom-atom interactions challenge positive-P simulations

Abstract

We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to the dynamics of dissociation of a molecular Bose-Einstein condensate (BEC) into correlated bosonic atom pairs. We also perform the same simulation using two stochastic phase-space techniques for quantum dynamics -- the positive P-representation method and the truncated Wigner method. By comparing the results of our calculations we are able to assess the relative strength of these theoretical techniques in describing molecular dissociation in one spatial dimension. An important aspect of our analysis is the inclusion of atom-atom interactions which can be problematic for the positive-P method. We find that the truncated Wigner method mostly agrees with the positive-P simulations, but can be simulated for significantly longer times. The pairing mean-field theory results diverge from the quantum dynamical methods after relatively short times.